Theme Essential Question: How are functions used to describe relationships that happen in our lives?
Essential Questions:
How can you describe a relationship given a piece-wise graph?
How do you sketch a piece-wise graph given a description?
Standards
8. F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Objectives
The student will interpret a situation, given a graph depicting a series of events.
The student will prepare a graph depicting the series of events, given a situation.
Assessment Product
Students will continue creating a portfolio detailing their growth pertaining to the topics addressed throughout this unit on functions. The Entry provided follows the theme of construction repair and remodel.
Entry #7
Students are to develop two piece-wise graphs with supporting explanations that depict a delivery truck supplying several job sites.
The first graph will describe the truck’s distance from the warehouse.
The second graph will describe the truck’s speed during the delivery trip. The truck will make at least 5 stops.
Key Questions
What do vertical, horizontal, increasing, and decreasing line segments represent in a distance vs. time graph?
What do vertical, horizontal, increasing, and decreasing line segments represent in a speed vs. time graph?
How would you apply your knowledge of interpreting graphs using a stock mark graph?
Observable Student Behaviors
The student can describe quantitatively a piece-wise function.
Given a verbal description, the student can sketch the corresponding piece-wise function.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Activities [see Legend to highlight MCO and HYS]
Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 2-7 p.57-60
ABC Mastering the Common Core in Mathematics 7.8, p. 101-104
Gizmo Lessons
Distance-Time Graph
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. (Student Exploration Sheet & Teacher Guide Available)
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. (Student Exploration Sheet & Teacher Guide Available)
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. (Student Exploration Sheet & Teacher Guide Available)
Teaching the Common Core Math Standards with Hands-On Activities by Judith Muschla
8.F.5 p.198
Diverse Learners
Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Algebra’scool: Unit C Module 9
Grade: 8 Unit: 3 Week: 7 Dates: 1/22-1/25 (4 days)
Content: Analyzing Functions
Theme Essential Question:
How are functions used to describe relationships that happen in our lives?
Essential Questions:
Standards
Objectives
Assessment
Product
- Students will continue creating a portfolio detailing their growth pertaining to the topics addressed throughout this unit on functions. The Entry provided follows the theme of construction repair and remodel.
Entry #7Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Functions, graphing functions, linear/non-linear
Suggested Activities [see Legend to highlight MCO and HYS]
- Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 2-7 p.57-60
- ABC Mastering the Common Core in Mathematics 7.8, p. 101-104
- Gizmo Lessons
- Distance-Time Graph
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. (Student Exploration Sheet & Teacher Guide Available)- Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. (Student Exploration Sheet & Teacher Guide Available)- Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. (Student Exploration Sheet & Teacher Guide Available)Diverse Learners
Odyssey (teacher discretion)
Skills Tutor (teacher discretion)
Algebra’scool: Unit C Module 9
Homework
Terminology for Teachers
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
Art, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
Websites
Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6